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Generalized Helicoid

The Surface generated by a twisted curve $C$ when rotated about a fixed axis $A$ and, at the same time, displaced Parallel to $A$ so that the velocity of displacement is always proportional to the Angular Velocity of Rotation.

See also Generalized Helix, Helicoid, Helix


do Carmo, M. P.; Fischer, G.; Pinkall, U.; and Reckziegel, H. ``General Helicoids.'' §3.4.3 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 36-37, 1986.

Fischer, G. (Ed.). Plate 89 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 85, 1986.

Kreyszig, E. Differential Geometry. New York: Dover, p. 88, 1991.

© 1996-9 Eric W. Weisstein